基于多项式插值的多部门限秘密共享方案
Multipartie Threshold Secret Sharing Scheme Based on Polynomial Interpolation
摘要: 在门限秘密共享方案中，一个参与者集合是否能恢复主秘密，取决于参与重构的参与者数量。在某种情况下，仅由一组参与者就能恢复主秘密，权限会相对过于集中。为了避免该问题，本文将一个大集合的参与者划分为几个不相交分区，每个分区都有一个独立部分访问结构；只有满足所有部分访问结构的参与者集合，才能恢复主秘密，否则得不到主秘密的任何信息。基于Shamir门限秘密共享方案和自由群中短词排序，本文构造了新的多部门限秘密共享方案，该方案可实现主秘密的动态更新，避免主秘密改变时分发阶段的通信需求，使整个方案在更新主秘密时更加高效。
Abstract: In the threshold secret sharing scheme, whether a set of participants can recover the secret de-pends on the number of participants participating in the reconstruction. In some cases, only one group of participants can recover the secret, and the authority will be relatively centralized. To avoid this problem, the participants of a large set are divided into several disjoint partitions, each partition has an independent part access structure; only the set of participants meeting all partial access structures can recover the secret, otherwise no information of the secret can be obtained. Based on Shamir threshold secret sharing scheme and shortlex order in the free group, this paper constructs a new multipart threshold secret sharing scheme. This scheme can realize the dynamic update of the secret, avoid the communication requirements of the time transmission phase when the secret changes, and make the whole scheme more efficient when updating the main secret.
文章引用：林苇婷, 林昌露. 基于多项式插值的多部门限秘密共享方案[J]. 理论数学, 2022, 12(12): 2124-2132. https://doi.org/10.12677/PM.2022.1212228

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